Okay, first, sorry if it's quite long. It's just quite complicated situation and I thought I'd give as many details as possible to maybe find the best solution.

There's the thing. I'm a very close friend of this family. the boy (now 13), wants to play drums ever since he was around 10 years old, though he kind of talked even earlier about his love for drums. His mother though insisted he better learn the guitar or any other instrument. She plays an acoustic guitar (though is not a professional), the daughter (now 17) plays bass guitar, keyboards and sings (and knows some guitar too), and the neighbours are tolerant of all this noise. I play both acoustic guitar and electric, and can frequently practice there (when I'm on a visit for a few days), and nobody ever has a problem with that. They are in a flat, but only have like two neighbours in the same house (a detached house with three flats).

she made him go to the music school last year, but he had to choose another instrument because there wasn't anymore space for new learners in a drum class. He learns the french horn. He seems okay with it for now, but it isn't really what he wishes to do. He said he's doing it just to show her he won't give up on an instrument, and so he can get drums. He was really good for the whole year, and finished his class with a B. They told he is very talented for both melodic and rhythm instruments.

The problem begins when anyone says anything about buying drums. It seems like she doesn't even care about the child's wishes. It was okay to buy her daughter a bass guitar, it was okay to get the guitars (there are three acoustics in the house) and synthesizer...

Reasons she complains:
1. The flat is too small and drums would use all the space.
We told her to measure the flat, so we can see what dimensions the drums should have that would not use all the space available She hasn't done it ever. We also told her he could disassemble the drums after practice and put them together again if they really were too big. She didn't even care to think about it.

2. The drums are too loud.
The neighbours are very tolerating and nobody ever complained about any noise during the day hours (till 10 p.m. as is the law), as neighbours play musical instruments too (though not the drums). it would work out somehow. If they really were too loud, we told her he could practice in some neighbour's house in the vicinity, as he is a drummer. She didn't even bother to ask.

3. The drums are too expensive.
We told her we could help save up the money, like both kids, me, some other friends, their father (doesn't live with them, but visits often and loves his kids), etc. And there are some good and quite cheap beginner sets, so money wouldn't really be a problem.

4. He wouldn't stick to the instrument and would want to quit fast
Well, he dreams about it for few years, plays every time he has an option to (when bands practice, whenever someone has drums...), he often plays around tables, chairs, etc., with drum sticks. He watches videos and plays videogames about drums. He is passionate about learning music and did stick to the horn for an entire year and made it with a B. He doesn't show obvious signs of quitting, as he loves learning about music, but would love the drums more though. Sometimes he tries to play guitar, and plays around with a keyboard. So this is not really a problem.

The boy has ADHD and lots of energy, but is known to stick and concentrate on to the things he is passionate about (hours of video games, playing instruments, football, etc), and music classes on drums would help him to release some of his energy while improving concentration.

Now, the boy has his 14th birthday in September and really worked hard both in school and music school to accomplish his goal of getting drum kit for birthday. Now we have a problem. She says she'd enroll him in a drum class (though again it is full, and she didn't even care to ask soon enough when there was time to get in), but that he won't have the drums at home and should care about where he would practice on his own.

I often bring my electric guitar over, and he really lights up when he sees it. He often says if there really wouldn't be any option to have or play drums (but there is), he'd like to play an electric guitar (he loves rock and metal music mostly). Again she says she doesn't wanna hear this loud sound every day, especially beginner's mistakes. She worries he would play too often, or play it too loud, etc. She has no problem seeing me play it (though I'm not a beginner anymore), but the thought of her kid playing this just sets her off, like she would have to listen everyday to the horrible sound. And said something like electric guitars are not "proper instruments" to learn (more like some "toys"), and that only acoustic guitars are. LOL

How could we convince his mom to respect her kid's wishes? To allow him get the drums, and to find some solution? To care enough to see what he is really passionate about and help him?

Anybody has any advice or experience on that matter? We really need some help here.
Thank you!

A multipad like an Octapad might be a good compromise? No volume or space issues, but it'll still teach a lot of the basic techniques, even more if you add a kick and/or hihat pedal. A complete electronic kit like a dtxplorer is also amazing bang for your buck. To sell it to the mom it's probably a great idea to look at having a family jam session every week, since there is bass and guitar too. Adding electronic percussion would be nice, I'd assume the volume is the real blocking issue. Music and a family jam band is a great way to interact with your kids. She probably doesn't know about electronic percussion though!